Initial semantics in logics with constructors

The constructor-based logics constitute the logical foundation of the so-called OTS/CafeOBJ method, a modelling, specification and verification method of the observational transition systems. The important role played in algebraic specifications by the initial algebras semantics is well known. Free models along presentation morphisms provide semantics for the modules with initial denotation in structured specification languages. Following Goguen and Burstall, the notion of logical system over which we build specifications is formalized as an institution. The present work is an institution-independent study of the existence of free models along sufficient complete presentation morphisms in logics with constructors in the signatures.